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1 Crystaldraw: a Computer Model to Model Crystal Structures, Axial And CrystalDraw: A Computer Model to Model Crystal Structures, Axial and Planar Channelling Directions and Crystal Alignment For Channelling Experiments J. England*1, A. Ellis, K. Piper Radiate Report R002 ABSTRACT To aid the understanding of crystallographic concepts, a C# computer programme “CrystalDraw” has been written to produce models of crystal structures and their associated axial and planar channelling directions in three-dimensions and to generate their corresponding two-dimensional projections. Visualisation of the models using specially written macros within Paraview illustrates how to orient and manipulate crystals for channelling measurements and guide interpretations of collected channelling data. INTRODUCTION This paper describes a programme, “CrystalDraw”, that generates and visualises crystal structures, their channelling directions and planes in three dimensions and relative to two dimensional projections and shows how to orient crystals on experimental goniometers. The source code is freely available by contacting the corresponding author and through the RADIATE program site [1] so that users can understand the concepts used to generate the visualisations and customise the program to describe experiments on a chosen crystal using the apparatus present in a specific laboratory. Visualisation of Crystallography Concepts This report is not intended to teach the concepts of crystallography as many excellent text books, such as Hammond [2], and on-line courses, such as Hoffmann & Sartor [3], already exist. However, the visualisation of crystallographic concepts for the novice can be difficult. Text books on crystallography, such as [2], repeatedly suggest the use of three dimensional models to aid the understanding of the reader. Making physical models can be a challenge and does not always easily illustrate a concept. The first motivation for producing the CrystalDraw programme was to produce a virtual 3D visualisation package in which a crystal structure can be generated and then inspected. Whilst there are many software packages and excellent websites already available that show crystal structures, the underlying assumptions used to produce the structures are not always accessible. By making the source code available, a second motivation was to allow the underlying mathematical methods and symmetry considerations used to generate the crystal structures to be understood. In this way concepts such as Bravais lattices, unit cells, equivalent positions (and perhaps in the future generation of the basis atoms from these) can be illustrated. Orientations of zone axes and planes as referenced by Miller indices (and in the future by Weber *Corresponding author: [email protected], Surrey Ion Beam Centre, Advanced Technology Institute, University of Surrey, Guildford, Surrey GU2 7XH, UK 1 symbols and Miiler-Bravais indices) can be plotted relative to the crystal lattice and atoms. Thirdly, and of importance for the ion beam community, CrystalDraw can be used as a 3D CAD tool to visualise real world problems applied to a generated crystal structure. Crystallographic information can be communicated through two dimensional methods such as stereographic projections. The authors initially had difficulty converting the information on a stereographic projection into instructions of how to manipulate a six- axis goniometer to align crystal samples to chosen axial and planar channelling directions. The literature also uses a variety of types of projection, so CrystalDraw can generate projections of stereographic, equiangular azimuthal and gnomic types. CrystalDraw allows alignment procedures to be visualised and hence experiments can be planned before committing accelerator time. Application to Ion Beam Analysis Channelling Rutherford Backscattering Spectroscopy (RBS/c) and related ion beam analysis (IBA) techniques such as channelling PIXE, NRA and ion transmission were first developed in the 1970s. An excellent review of the first 50 years of channelling IBA has been given by Vantomme [4]. In these techniques, the spectroscopic yield is measured as the direction of a primary ion beam towards a crystalline sample is varied around a channelling direction. To extract the information from channelling curves the experimenter must first be convinced that features in the channelling dip are due to material properties and not from experimental artefacts. This requires a thorough understanding of the experiment and confidence that the crystal is aligned as intended. Hence a fourth motivation for developing CrystalDraw was to understand scanning directions considered in experiments. The theory of ion channelling using the “string model” approach has been described by Feldman et al [5], amongst others. Whilst CrystalDraw calculates channel angular half widths and minimum yields to aid channel identification, we have used FLUX [6,7] to model measured dips in detail to extract material information or to investigate small experimental misalignments. It is our intention to evaluate other programs such as McChasy [8] and RBSADEC [9] in the future. The RBS/c technique is complementary to other crystallography measurements such as those collected using transmission electron microscopy (TEM) and x-ray diffraction (XRD) [4]. RBS/c is particularly sensitive to crystal imperfections. The primary beam cross sectional dimensions, typically a few mm but possibly down to a few nm, limits the spatial resolution to those dimensions and measurements average the sample characteristics under the beam irradiation area. RBS/c can detect point defects (such as interstitial atoms) and extended defects (such as stacking faults and lattice strain). The flux focussing nature of channelling makes defect detection very sensitive. By measuring along different channels, defect positions within the crystal lattice can be determined and by analysing within specific ranges of the scattered ion energies, RBS/c is also capable of measuring crystal qualities for different component elements at different depths in the crystal. TEM on the other hand, using electron beams focussed to a few nm, has a much higher spatial resolution than RBS/c but can only probe a sample area within a lamella (for cross sections) which are typically a few microns wide and few nm thick or within a field of view of a few microns for top down techniques. Point defects are not usually visible by TEM. XRD is strongly influenced 2 by the order of the crystal lattice and is a reference technique to determine crystal lattice constants. X-ray beam sizes are similar to the RBS/c ion beam dimensions but the depth of penetration of the x-rays is deeper (many microns) than ions. Although XRD does not inherently have any depth resolution, when a characteristic peak can be assigned to a particular element, it may be assigned to having arisen from reflections from a particular compositional layer of a sample. The widths of refraction peaks can also give information about variations in atomic positions and hence lattice disorder. RBS/c is most informative when considered in combination with these complementary techniques and other sources of information about the sample [4]. Previous Work In addition to those cited above, the following references were used extensively in preparing CrystalDraw: Doyle and co-workers at Sandia National Laboratories built on earlier work (especially Gemmel [10]) to produce papers and an associated excel worksheet that calculates half widths and yield minima for planar and axial channels [11-13]. Some examples of stereographic (actually azimuthal equi-angular) projections are included in the worksheet but the code used to generate them was not available. The calculations used look up tables for cubic crystals; we wanted to generate this information from first principles so that CrystalDraw should work for any crystal system. Much of the information used above is also included in Appendix 17 of the Handbook of Modern Ion Beam Materials Analysis [14] which also includes methods for aligning crystals on goniometers. The “Ion Implantation Technology Conference School Book” [15] has a detailed chapter on channelling and stereographic projections but is slightly confusing in showing stereographic and gnomic projections. This report describes the uses of CrystalDraw. Details of the C# code and python macros used within the Paraview visualisation programme are described in the appendix. 3 DESCRIPTIONS OF VISUALISATIONS Step 1 – Crystal Structure CrystalDraw creates crystal structures from crystal information files (CIF) that can be downloaded from the Crystallography Open Database [16]. Each CIF contains the symmetry information, lattice angles and dimensions as given in the International Tables for Crystallography which is available as a hypertext book on line [17] and the structures are well presented on another site [18]. This paper uses GaAs (case 9008845 in the database) as an example crystal. This form of GaAs (Space Group 216 “F-43m”) has the zinc blende structure, which is based on a face centred cubic structure. Si (case 9008565) has a similar structure, but the single type of atom moves Si into Space Group 227 “Fd3m”. CrystalDraw takes the information from the CIF file to generate the Bravais Lattice and atoms at the equivalent symmetry points. From this, the atoms within the unit cell can be visualised (Fig 1). A large crystal formed from a set of unit cells can also be shown so that channels can be visualised when orienting the crystal (see Fig 2). In this paper, the large
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